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I've written a system for learning basic algebra which has you solve problems by clicking on the rules of basic algebra (commutativity, associativity, etc.). It is impossible to make mistakes because the machine checks things like correct handling of division by zero. Each step is justified, so each solution serves as a formal proof. Right now it handles algebra up to quadratic equations and simultaneous equations.

It is intended to be a computer proof system anyone can learn. The style of mathematics presented mimics equation solving on a blackboard, so it should be familiar to everyone.